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首页> 外文期刊>Statistics and computing >Introduction to 'On a class of σ-stable Poisson-Kingman models and an effective marginalized sampler' by S. Favaro, M. Lomeli, Y. W. Teh
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Introduction to 'On a class of σ-stable Poisson-Kingman models and an effective marginalized sampler' by S. Favaro, M. Lomeli, Y. W. Teh

机译：S. Favaro，M。Lomeli，Y。W. Teh介绍的“关于一类σ稳定的Poisson-Kingman模型和有效边缘化采样器”

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The paper introduces a practicable alternative to the ubiquitous Dirichlet process (DP) mixture model that has dominated the nonparametric Bayesian literature over the past 20 years and more. Nonparametric Bayesian inference can be characterized as inference in infinite-dimensional parameter spaces. One of the standard inference problems is density estimation. That is, assuming a random sample y_i ～ F,i = l,...,n, the inference goal is to estimate the unknown distribution F. If F is assumed to be in some parametric family of probability models that can be indexed by a finite-dimensional vector of parameters, for example, F ∈ [F_θ,θ ∈ (R)~k}, then the problem reduces to parametric inference. However, in many problems it is unreasonable or undesirable to restrict F to a parametric family. Bayesian inference requires that we complete the model with a prior probability model on the unknown quantity, in this case, the random distribution F. That is, we need a nonparametric Bayesian prior model p(F). The arguably most popular prior probability model p(F) for random distributions is the DP prior prior (Ferguson 1983). See, for example, Ghoshal (2010) for a recent review of the DP prior and related constructions. It could be argued that the DP is to nonparametric Bayesian inference what the normal distribution is to parametric inference. In the sense that the DP appears as a special case for several other, more general models. In particular the DP is a special case of stick-breaking priors (Ishwaran and James 2001). And it is a special case of normalized random measures (Regazzini et al. 2002). A good recent review appears in Lijoi and Priinster (2010).
机译：本文介绍了一种可行的替代方法，该方法可替代普遍存在的Dirichlet过程（DP）混合模型，该模型在过去20多年或更长时间里一直主导着非参数贝叶斯文献。非参数贝叶斯推理可被描述为无限维参数空间中的推理。标准推断问题之一是密度估计。也就是说，假设一个随机样本y_i〜F，i = l，...，n，则推断目标是估计未知分布F。如果假定F在某个参数族概率模型中，则可以用参数的有限维向量，例如F∈[F_θ，θ∈（R）〜k}，则问题简化为参数推论。但是，在许多问题中，将F限制为参数族是不合理的或不希望的。贝叶斯推断要求我们使用未知量的先验概率模型（在这种情况下为随机分布F）来完成模型。也就是说，我们需要非参数贝叶斯先验模型p（F）。可以说，最流行的随机分布先验概率模型p（F）是DP先验先验（Ferguson 1983）。参见，例如，Ghoshal（2010）对DP先验和相关构造的最新评论。可以说，DP对非参数贝叶斯推断而言，正态分布对参数推断而言。从某种意义上说，DP在其他几种更通用的型号上是特例。特别是DP是先验先破的特例（Ishwaran and James 2001）。这是归一化随机测度的特例（Regazzini等，2002）。 Lijoi和Priinster（2010）发表了一篇不错的近期评论。

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  • 来源
    《Statistics and computing》 |2015年第1期|65-66|共2页
  • 作者

    Peter Mueller;

  • 作者单位

    Department of Mathematics, University of Texas, Austin, TX 78712, USA;

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